The ordering of the set of tuples is arbitrary, but the features \(\mathbf {f}_m\)  consist of the density \(\alpha _{i,j,k}\)  and radiance colors \(\rho _{i,j,k}\)  at that location \(\mathbf {c}_m= (i,j,k)\) . For the radiance field colors, we use the spherical harmonics proposed in Plenoxels [1]} for view-dependent learning of radiance common in NeRFs [2]}. The SRF can be viewed as a distillation of the NeRF MLP into sparse voxels for efficient optimization and volume rendering.
In many 3D object tasks, a coarse-to-fine approach is followed, demanding multiple resolutions. Hence, we collect the SPARF with multiple resolutions \(H\in \lbrace 32,128,512\rbrace \) , as shown in Figure REF . We used an adaptation of Plenoxels [1]} to collect the dataset of a total of one million SRFs as we detail next. In order to scale up the Plenoxels optimization for this huge number of shapes and variants, we utilize a large number of images in the SPARF dataset to reduce the iterations to a minimum number while maintaining a high average PSNR across the dataset for the collected SRFs across the multiple resolutions. A total of 200K GPU hours are used in the optimization process to collect SPARF. highly detailed 3D meshes can be extracted easily from the collected SRFs as can be seen in Figure REF .
